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%I #38 Feb 12 2019 04:15:26
%S 19,41,61,89,149,419,461,491,619,641,691,941,1489,4691,4861,6481,6491,
%T 6841,8419,8461,8641,8941,9461,14869,46819,48619,49681,64189,64891,
%U 68491,69481,81649,84691,84961,86491,98641
%N Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.
%C There are only 36 terms in this sequence, which is a finite subsequence of A152313.
%C Two particular examples:
%C 6481 is also the smallest prime formed from the concatenation of two consecutive squares.
%C 81649 is the only prime containing all the nonprime positive digits such that every string of two consecutive digits is a square.
%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=81649">81649</a>, Prime Curios!
%e 14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.
%t Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* _Michael De Vlieger_, Jan 19 2019 *)
%o (PARI) isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ _Michel Marcus_, Jan 14 2019
%Y Subsequence of A152313. Subsequence of A029743. Subsequence of A155024 (with distinct nonprime digits but with 0) and of A034844.
%Y Cf. A029743 (with distinct digits), A124674 (with distinct prime digits), A155045 (with distinct odd digits), A323387 (with distinct square digits), A323578 (with distinct digits for which parity of digits alternates).
%K nonn,base,fini,full
%O 1,1
%A _Bernard Schott_, Jan 13 2019
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